   Chapter 15, Problem 8RQ

Chapter
Section
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.The integral ∭ E k r 3   d z   d r   d θ represents the moment of inertia about the z-axis of a solid E with constant density k.

To determine

Whether the statement, “The integral Ekr3dzdrdθ represents the moment of inertia about z-axis of a solid E with constant density k” is true or false.

Explanation

Given:

Density ρ(x,y,z) is constant say k.

Formula used:

The moments of inertia about z-axis is given by,

Iz=liml,m,ni=1lj=1mk=1n(x2+y2)ρ(xij*,yij*,zij*)ΔV=E(x2+y2)ρ(x,y,z)dA

If f is a polar rectangle R given by 0arb,αθβ, where 0βα2π , then, R

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